Many measurements of interest are generated by applying a repetitive signal to a device under test (DUT) and measuring the frequency response of the output of the DUT. In one common configuration, the output of the DUT is down converted in a mixer to an IF signal that is digitized by an analog-to-digital converter (ADC). The ADC output is then transformed using a FFT to provide a measurement of the amplitudes and phases of the tones in the output signal. The tones will be separated by a frequency that is determined by the repetition rate of the input signal. If the measurement is repeated, the amplitude of the tones and their frequencies will remain the same to within the experimental errors. Hence, spectra that depend only on the amplitude of the tones can be compared from time to time.
The phases of the tones as a function of frequency depend on the starting time of the sample sequence digitized by the ADC relative to some fixed starting point of the repetitive sequence. If this time changes, the phases as a function of frequency also change. Hence, comparing two phase measurements taken at different times presents significant challenges. For many measurements, it is the relationship between the phases as a function of frequency that is of interest. In these cases, normalization procedures are used to generate a set of normalized phases that are independent of the time the ADC sequence starts relative to the repetitive signal and in which the desired relationship can be examined.
However, there are measurements in which two different frequency spectra are measured at different times, and the problems associated with the phases of the tones cannot be easily overcome by a simple phase normalization process.